17. (a) If the system of three charges is to be in equilibrium, the force on each charge
must be zero. The third charge
q
3
must lie between the other two or else the forces acting
on it due to the other charges would be in the same direction and
q
3
could not be in
equilibrium. Suppose
q
3
is at a distance
x
from
q
, and
L
–
x
from 4.00
q
. The force acting
on it is then given by
()
33
3
2
2
0
4
1
4
qq
qq
F
x
Lx
πε
§·
=−
¨¸
−
©¹
where the positive direction is rightward. We require
F
3
= 0 and solve for
x
. Canceling
common factors yields 1/
x
2
= 4/(
L
–
x
)
2
and taking the square root yields 1/
x
= 2/(
L
–
x
).
The solution is
x
=
L
/3.
The force on
q
is
2
3
22
0
14
.
0
0
.
4
q
qq
q
F
xL
ε
−
=+
π
The signs are chosen so that a negative force value would cause
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 Spring '09
 Bolton
 Charge, Force

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